Answer:
2/3V
Explanation:
Given that a ball of mass M and speed V collides with another ball of mass 2M and velocity v/2 . After collision they stick together and we need to find their speed after collision . According to Law of Conservation of Momentum , The total momentum of the system before and after collision is constant .That is ;
[tex]\sf\qquad\longrightarrow m_1u_1+m_2u_2=m_1v_1+m_2v_2\\ [/tex]
[tex]\sf\qquad\longrightarrow MV + 2M\bigg(\dfrac{V}{2}\bigg) = (2M + M)(v)\\ [/tex]
[tex]\sf\qquad\longrightarrow MV +MV= 3Mv\\[/tex]
[tex]\sf\qquad\longrightarrow 2MV = 3Mv\\ [/tex]
[tex]\sf\qquad\longrightarrow v =\dfrac{2M}{3M}V\\ [/tex]
[tex]\sf\qquad\longrightarrow \pink{ v_{after\ collision}=\dfrac{2}{3}V }[/tex]
Hence the velocity after the collision ia 2/3V .
